Microelectromechanical system (“MEMS”) resonators are small electromechanical structures that vibrate at high frequencies and are often used for timing references, signal filtering, mass sensing, biological sensing, motion sensing, and other applications. MEMS resonators are considered a common alternative to quartz timing devices to provide an accurate time or frequency reference. In general, quartz resonators have a high quality factor and piezoelectric coupling. High quality factor indicates a low rate of energy loss relative to the stored energy of the resonator, i.e., the oscillations die out more slowly. However, one limitation for quartz resonators is that they are difficult to design in smaller sizes.
Typically, MEMS resonators are made of silicon using lithography based manufacturing processes and wafer level processing techniques. Designers and manufacturers have found that pure silicon resonators often demonstrate very high quality factors comparable to quartz crystals. However, bare silicon is not piezoelectric and pure silicon resonators have high motional impedance making them unsuitable to replace quartz resonators in many applications.
In order to lower the motional impedance of MEMS resonator, some designs have added piezoelectric material, such as a layer of thin film of aluminum nitride (AlN). A typical piezoelectric micromechanical resonator is shown in FIGS. 1A and 1B.
In particular, FIG. 1A illustrates a top view of a conventional resonator 10 that is rectangular shaped and includes two smalls anchor 11A and 11B on the sides of the resonator to mount the resonator.
FIG. 1B illustrates a cross sectional view of the conventional resonator 10. Typically, the resonator 10 is manufactured of silicon using MEMS manufacturing techniques. On top of silicon substrate 12, the resonator 10 has a piezoelectric thin film 16 sandwiched between two metal electrodes 14A and 14B to provide piezoelectric coupling. In an exemplary design, the metal electrodes 14A and 14B are typically molybdenum, but other materials such as platinum or aluminum may also be used. Moreover, the piezoelectric film 16 may be aluminum nitride (AlN) or doped aluminum nitride, but may also be PZT or titanium oxide.
In conventional designs, the thickness of the metal electrodes 14A and 14B is typically 50 nanometers (nm) to 400 nm and the thickness of the piezoelectric film 16 is typically 400 nm to 2 um. Moreover, the thickness of the silicon substrate 12 may range from 3 μm to 30 μm, for example. Although not shown, additional thin film layers may also be present in some conventional designs. For example, a layer of silicon dioxide thin film can be used to change the temperature coefficient of frequency of the resonator.
To maximize the resonator quality factor, resonators are preferably designed to resonate in a bulk mode where the resonator deforms mainly in the in-plane vibration mode where the out-of-plane movement is minimized. In particular, it is desirable that out-of-plane bending modes of the resonator are avoided since these modes have low quality factors at high frequencies.
In general, lateral dimensions of resonators will determine the resonator's resonance frequency and are also important in designing high quality factor resonators. Typically, a resonator with a high quality factor has a rectangular shape with width W and length L, for example as shown in FIG. 2. In particular, FIG. 2 illustrates a top view of a width extensional resonator 10 according to a conventional design. As shown, the vibrational motion of the resonator 10 is mainly in the width direction (i.e., contraction and expansion vibration). This width extensional mode is preferred since the anchoring points 11A and 11B on the short sides of the resonator have minimal movement, thereby minimizing the anchor losses and maximizing the quality factor.
Moreover, it is known that certain aspect ratios (“AR”), defined as the ratio of length L to width W (i.e., AR=L/W), minimize the mounting losses and therefore maximize the quality factor, for example, as described in Patent Document 1, identified below. In particular, an optimal aspect ratio ranges from 1.2 to 1.8 depending on material properties and is typically around 1.5 for silicon based resonators.
Furthermore, the resonance frequency is inversely related to the resonator width. Thus, as the width and length of the resonator 10 is reduced, the resonant frequency is correspondingly increased. However, the small size of such a resonator will result in higher electrical impedance that is undesirable. One way to reduce the electrical impedance of a high frequency resonator is to increase the aspect ratio by an integer multiple N so that the aspect ratio is approximately N×1.5 (with 1.5 being an example of an optimal aspect ratio). For example, good choices for the aspect ratio are 1.5, 3.0, 4.5, 6.0, 7.5, and so on, with the exact value that minimizes the anchor movement being determined by simulation or experiments.
Moreover, the resonator impedance can be decreased even further by combining two or more rectangular shaped resonators along the long edge to make a higher order overtone resonator, as described in Non-patent Document 1, for example, identified below.
FIG. 3A illustrates a higher order overtone resonator according to a conventional design. As shown, the resonator design includes four plate resonators 10A, 10B, 10C and 10D, with the resonator outer shape for each resonator being rectangular with a length L and a width W that is selected to achieve an aspect ratio AR=L/W=6. Moreover, FIG. 3B illustrates the resulting overtone resonator 20 according to the conventional design shown in FIG. 3A. As shown, the four resonators 10A-10D are connected and aligned along the long edge with length L to make a fourth-order overtone width-extensional mode resonator. Although four resonators are shown for this design, the technique can be extended to even higher order, for example, where 50 or even 100 or more plates can be connected together in this manner. Of course, one obvious drawback of this approach is that as the overall resonator dimensions become large, which, in turn, increases the number of undesirable out-of-plate bending modes during operation. These modes may be close in frequency to the desired in-plane mode and can result in spurious impedance response.
FIG. 3C illustrates an electrode pattern for the overtone resonator 20 shown in FIG. 3B. As shown, resonators 10A and 10C share the same top electrode 22A (i.e., top electrode 1) and resonators 10B and 10D share another top electrode 22B (i.e., top electrode 2). It is known that many different electrode patterns can be employed, for example, as disclosed in Patent Document 2, identified below.
FIGS. 4A and 4B illustrate graphs of exemplary electrical resonator responses. The electrical responses are shown as impedance to frequency. As shown, for example, a clean impedance curve is illustrated in FIG. 4A where one clear resonance is observed. In contrast, a spurious impedance curve is shown in FIG. 4B where an additional spurious resonance is observed following the main resonance. This type of spurious response is due to bending modes near the main width-extensional mode and it is very detrimental to resonator performance in time and frequency applications. Moreover, the resonance frequency of the out-of-plate bending modes is sensitive to small manufacturing variations and it may not be possible to completely eliminate these modes around the main resonance by adjusting the resonator thickness and aspect ratio. In manufacturing, this may result in yield loss where some resonators work as desired and some resonators exhibit the undesirable spurious response.
Patent Document 1: U.S. Pat. No. 5,548,180.
Patent Document 2: WO 2016/114237.
Non-patent Document 1: Ho, et al., “High-order composite bulk acoustic resonators”, Micro Electro Mechanical Systems, 2007. IEEE 20th International Conference on. IEEE, 2007.